GENEVA — The top human rights official of the United Nations took China to task Friday over suppression of the rights of Tibetans, which she said had driven them to ‘‘desperate forms of protest,’’ referring to some 60 self-immolations by Tibetans protesting Chinese rule that have been reported since March 2011, including seven since mid-October.

Navi Pillay, the high commissioner for human rights, said in a statement that she was disturbed by reports of detentions, disappearances, and excessive use of force against peaceful demonstrators, as well as curbs on Tibetans’ cultural rights.

Pillay said she had ‘‘several exchanges’’ with the Chinese government on the issue and her rare public criticism of Beijing’s conduct on human rights appeared to reflect a measure of frustration.

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‘‘We felt the time had come to talk publicly about that,’’ a spokesman for Pillay, Rupert Colville, said Friday in Geneva.

“More needs to be done to protect human rights and prevent violations,’’ Pillay said in the statement, urging China to release Tibetans who had been detained merely for exercising such fundamental rights as freedom of expression, association, and religion.